A device for protecting against the scouring of granular fillings submerged in gravity structures in which a filling with granular materials must be deposited once the structures are submerged, so that the structures reach a weight sufficient to en sure the stability thereof against the actions to which they are subjected. The device consists of one or more porous covers that sit and/or are secured as an upper closure of the structure to protect the inner filling, each of the covers having a plurality of openings that are distributed on the surface thereof and have a size suitable to allow the passage of the filling material, which filling material is transferred to the inside of the structure simply by pouring until a height close to the cover is reached, leaving a margin or chamber between the two that is suitable for generating an internal turbulence that dissipates wave energy and incident currents, thereby making it difficult for the filling material to escape from the inside through the openings.